Spectral Duality in Integrable Systems from AGT Conjecture

Abstract

We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality.

References in corpus (7)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Towards a proof of AGT conjecture by methods of matrix models
• Quantum Painleve-Calogero Correspondence
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

Cited by in corpus (55)

• On Three Dimensional Quiver Gauge Theories and Integrability
• Ding-Iohara-Miki symmetry of network matrix models
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Anomaly in RTT relation for DIM algebra and network matrix models
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• Decomposing Nekrasov Decomposition
• A slow review of the AGT correspondence
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Rational Top and its Classical R-matrix
• Planck Constant as Spectral Parameter in Integrable Systems and KZB Equations
• On elementary proof of AGT relations from six dimensions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Higgsed network calculus
• Wall Crossing Invariants: from quantum mechanics to knots
• R-matrix-valued Lax pairs and long-range spin chains
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Three-particle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
• The MacMahon R-matrix
• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Seiberg-Witten curves and double-elliptic integrable systems
• 3d Mirror Symmetry from S-duality
• Generalized model of interacting integrable tops
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Confinement and Mayer cluster expansions
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• On complete solution of the quantum Dell system
• Quantum Integrable Systems from Supergroup Gauge Theories
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Can tangle calculus be applicable to hyperpolynomials?
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Notes on Mayer Expansions and Matrix Models
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• On the status of DELL systems
• Tau-functions for Quiver Gauge Theories
• Modular properties of 6d (DELL) systems
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• On generalized Macdonald polynomials
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• di-Langlands correspondence and extended observables
• Characteristic determinant and Manakov triple for the double elliptic integrable system
• Bispectral duality and separation of variables from surface defect transition
• Quantum spectral curve for (q,t)-matrix model
• Five-dimensional gauge theories and the local B-model
• Solution of quantum integrable systems from quiver gauge theories
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality
• Large N limit of spectral duality in classical integrable systems